I have been trying to calculate the distances to the spiral arms (neutral Hydrogen clouds) and our equation seems to work perfectly for longitudes 0<l<90 but doesn't seem to work for the outer galaxy (i.e. between 90<l<270) - we get distances but they're not correct. After reading a lot of literature online it seems the outer distances should actually be easier to calculate given that there would only be one solution, rather than two like in the inner galaxy. I'm using the tangent point method and the equation I am using to calculate the distance from the centre of the galaxy to the cloud is R = (Vsun*Rsun*sin(l))/(Vobs+Vsun*sin(l)) where Vsun is the velocity of the sun, Rsun is the distance from the Sun to the galactic centre. Vobs is calculated from the Doppler Effect using Vobs = c*(1-f'/1420.405...) - vlsr where c is the speed of light, f' is the observed frequency and 1420.405... is the frequency of the Hydrogen emission. I then use my R and calculate the distance d from the Sun to the cloud using d = Rsun*cos(l)±√((Rsun*cos(l))^2 - Rsun^2 + R^2) As said before, this all seems to work fine for 0<l<90, but not for l>90. The only thought I have had is that the way I have defined Vobs (defined as the velocity of the cloud along the line of sight minus the velocity of the Sun along the line of sight) might be true for all l<90, but not necessarily true for l>90 - for some longitudes and distances (i.e between 90<l<270), Vobs may become negative as the cloud is now moving towards us, instead of away. Any help with this is appreciated, thanks!